{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# scikit-learn-k-means"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Credits: Forked from [PyCon 2015 Scikit-learn Tutorial](https://github.com/jakevdp/sklearn_pycon2015) by Jake VanderPlas"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn; \n",
    "from sklearn.linear_model import LinearRegression\n",
    "from scipy import stats\n",
    "import pylab as pl\n",
    "\n",
    "seaborn.set()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## K-Means Clustering"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "('Reduced dataset shape:', (150, 2))\n",
      "Meaning of the 2 components:\n",
      "0.362 x sepal length (cm) + -0.082 x sepal width (cm) + 0.857 x petal length (cm) + 0.359 x petal width (cm)\n",
      "-0.657 x sepal length (cm) + -0.730 x sepal width (cm) + 0.176 x petal length (cm) + 0.075 x petal width (cm)\n"
     ]
    },
    {
     "data": {
      "image/png": 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Yu5+jX3/Lsb17aXcxGxeTSkK/Njz/xXzc3NzsEb2wgp49rVOp62fHju1i0mTL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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10c2dabd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn import neighbors, datasets\n",
    "\n",
    "iris = datasets.load_iris()\n",
    "\n",
    "X, y = iris.data, iris.target\n",
    "from sklearn.decomposition import PCA\n",
    "pca = PCA(n_components=2)\n",
    "pca.fit(X)\n",
    "X_reduced = pca.transform(X)\n",
    "print(\"Reduced dataset shape:\", X_reduced.shape)\n",
    "\n",
    "import pylab as pl\n",
    "pl.scatter(X_reduced[:, 0], X_reduced[:, 1], c=y,\n",
    "           cmap='RdYlBu')\n",
    "\n",
    "print(\"Meaning of the 2 components:\")\n",
    "for component in pca.components_:\n",
    "    print(\" + \".join(\"%.3f x %s\" % (value, name)\n",
    "                     for value, name in zip(component,\n",
    "                                            iris.feature_names)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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5deoYEyd1xsXFkVUrv2TQoOk4OjraInxhBX0njoeJ1ptfeteCxTS5MbmJFoV6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\nrQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x105f65390>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.cluster import KMeans\n",
    "k_means = KMeans(n_clusters=3, random_state=0) # Fixing the RNG in kmeans\n",
    "k_means.fit(X)\n",
    "y_pred = k_means.predict(X)\n",
    "\n",
    "pl.scatter(X_reduced[:, 0], X_reduced[:, 1], c=y_pred,\n",
    "           cmap='RdYlBu');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "K Means is an algorithm for **unsupervised clustering**: that is, finding clusters in data based on the data attributes alone (not the labels).\n",
    "\n",
    "K Means is a relatively easy-to-understand algorithm.  It searches for cluster centers which are the mean of the points within them, such that every point is closest to the cluster center it is assigned to.\n",
    "\n",
    "Let's look at how KMeans operates on the simple clusters we looked at previously. To emphasize that this is unsupervised, we'll not plot the colors of the clusters:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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YwKc+NYiysjJqaibR3r6F3bsrbMscen9E8kEBWCQL8tVn59T67hmVTPdtbqfD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\nwMSmAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10c5b1d10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.datasets.samples_generator import make_blobs\n",
    "X, y = make_blobs(n_samples=300, centers=4,\n",
    "                  random_state=0, cluster_std=0.60)\n",
    "plt.scatter(X[:, 0], X[:, 1], s=50);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "By eye, it is relatively easy to pick out the four clusters. If you were to perform an exhaustive search for the different segmentations of the data, however, the search space would be exponential in the number of points. Fortunately, there is a well-known *Expectation Maximization (EM)* procedure which scikit-learn implements, so that KMeans can be solved relatively quickly."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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m4CGm9xvYZH1bg0/HjvzuNkzc02g0vDz9IUwmE2VlBpydXRodfRAEoflEAL6L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\nEEIIJ5AELIQQQjjB/wPUisdaqVvQjwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10c597fd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.cluster import KMeans\n",
    "est = KMeans(4)  # 4 clusters\n",
    "est.fit(X)\n",
    "y_kmeans = est.predict(X)\n",
    "plt.scatter(X[:, 0], X[:, 1], c=y_kmeans, s=50, cmap='rainbow');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The algorithm identifies the four clusters of points in a manner very similar to what we would do by eye!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The K-Means Algorithm: Expectation Maximization\n",
    "\n",
    "K-Means is an example of an algorithm which uses an *Expectation-Maximization* approach to arrive at the solution.\n",
    "*Expectation-Maximization* is a two-step approach which works as follows:\n",
    "\n",
    "1. Guess some cluster centers\n",
    "2. Repeat until converged\n",
    "A. Assign points to the nearest cluster center\n",
    "B. Set the cluster centers to the mean \n",
    "   \n",
    "Let's quickly visualize this process:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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QZsE2r3Fzc+X/fu/Nis8Wk37MAZkcvNsX8fqcQTg6Ot5Tfe5m76Yj6D5ohl/BjcQHZi84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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10d30d2d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from fig_code import plot_kmeans_interactive\n",
    "plot_kmeans_interactive();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This algorithm will (often) converge to the optimal cluster centers."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### KMeans Caveats\n",
    "\n",
    "* The convergence of this algorithm is not guaranteed; for that reason, by default scikit-learn uses a large number of random initializations and finds the best results.\n",
    "\n",
    "* The number of clusters must be set beforehand.  There are other clustering algorithms for which this requirement may be lifted."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}
